A sulfur oxide storage material contains a magnesium-aluminum spinel (MgO.Al.sub.2 O.sub.3) and can be used as a so-called "sulfur trap" to remove sulfur oxides from oxygen-containing exhaust gases of industrial processes. In particular, it can be used for the catalytic purification of exhaust gas from internal-combustion engines to remove the sulfur oxides from the exhaust gas in order to protect the exhaust gas catalysts from sulfur poisoning. The material displays a molar ratio of magnesium oxide to aluminum oxide in the range of over 1.1:1, and the magnesium oxide present in stoichiometric excess is homogeneously distributed in a highly disperse form in the storage material.